A wind turbine has a rotor diameter of $70, m$ , wind speed of $10, m/s$ , power coefficient $0.45$ and air density $1.225, kg/m^{3}$ . Calculate the mechanical power intercepted by the rotor in MW.

hard 5 marks Class 10 · Geography · Minerals and Energy Resources

Answer

1.06 MW (approx)

The correct answer is 1.06 MW (approx) — Convert to MW: $1, 061, 190/1 0^{6} a pp r o x 1.06$ MW.

Step-by-step solution

Find radius: $r = \frac{70}{2} = 35$ m.
Compute rotor area: $A = π r^{2} = π \times 3 5^{2} \approx 3848.45$ m².
Use power formula: $P = 0.5, ρ, A, V^{3}, C_{p}$ .
Substitute values: $0.5 \times 1.225 \times 3848.45 \times 1 0^{3} \times 0.45$ .
First compute $0.5 \times 1.225 = 0.6125$ .
Then $0.6125 \times 3848.45 \approx 2358.2$ .
$2358.2 \times 1000 = 2, 358, 200$ .
$2, 358, 200 \times 0.45 \approx 1, 061, 190$ watts.
Convert to MW: $1, 061, 190/1 0^{6} a pp r o x 1.06$ MW.

Common mistake: Using diameter instead of radius to calculate area

Concept tested: Wind energy power calculation